'The total return on a portfolio of investments takes into account not only the capital appreciation on the portfolio, but also the income received on the portfolio. The income typically consists of interest, dividends, and securities lending fees. This contrasts with the price return, which takes into account only the capital gain on an investment.'

Using this definition on our asset we see for example:- The total return, or performance over 5 years of ProShares UltraPro QQQ is 428.4%, which is higher, thus better compared to the benchmark SPY (103.4%) in the same period.
- Looking at total return, or increase in value in of 35.5% in the period of the last 3 years, we see it is relatively larger, thus better in comparison to SPY (33.4%).

'The compound annual growth rate (CAGR) is a useful measure of growth over multiple time periods. It can be thought of as the growth rate that gets you from the initial investment value to the ending investment value if you assume that the investment has been compounding over the time period.'

Applying this definition to our asset in some examples:- Looking at the compounded annual growth rate (CAGR) of 39.5% in the last 5 years of ProShares UltraPro QQQ, we see it is relatively higher, thus better in comparison to the benchmark SPY (15.3%)
- Looking at compounded annual growth rate (CAGR) in of 10.7% in the period of the last 3 years, we see it is relatively greater, thus better in comparison to SPY (10.1%).

'Volatility is a statistical measure of the dispersion of returns for a given security or market index. Volatility can either be measured by using the standard deviation or variance between returns from that same security or market index. Commonly, the higher the volatility, the riskier the security. In the securities markets, volatility is often associated with big swings in either direction. For example, when the stock market rises and falls more than one percent over a sustained period of time, it is called a 'volatile' market.'

Which means for our asset as example:- Looking at the historical 30 days volatility of 74.7% in the last 5 years of ProShares UltraPro QQQ, we see it is relatively greater, thus worse in comparison to the benchmark SPY (20.9%)
- Compared with SPY (17.3%) in the period of the last 3 years, the volatility of 68.5% is larger, thus worse.

'The downside volatility is similar to the volatility, or standard deviation, but only takes losing/negative periods into account.'

Applying this definition to our asset in some examples:- The downside deviation over 5 years of ProShares UltraPro QQQ is 53%, which is higher, thus worse compared to the benchmark SPY (14.9%) in the same period.
- Compared with SPY (12.1%) in the period of the last 3 years, the downside risk of 48.1% is greater, thus worse.

'The Sharpe ratio is the measure of risk-adjusted return of a financial portfolio. Sharpe ratio is a measure of excess portfolio return over the risk-free rate relative to its standard deviation. Normally, the 90-day Treasury bill rate is taken as the proxy for risk-free rate. A portfolio with a higher Sharpe ratio is considered superior relative to its peers. The measure was named after William F Sharpe, a Nobel laureate and professor of finance, emeritus at Stanford University.'

Using this definition on our asset we see for example:- Compared with the benchmark SPY (0.61) in the period of the last 5 years, the Sharpe Ratio of 0.5 of ProShares UltraPro QQQ is smaller, thus worse.
- During the last 3 years, the risk / return profile (Sharpe) is 0.12, which is lower, thus worse than the value of 0.44 from the benchmark.

'The Sortino ratio improves upon the Sharpe ratio by isolating downside volatility from total volatility by dividing excess return by the downside deviation. The Sortino ratio is a variation of the Sharpe ratio that differentiates harmful volatility from total overall volatility by using the asset's standard deviation of negative asset returns, called downside deviation. The Sortino ratio takes the asset's return and subtracts the risk-free rate, and then divides that amount by the asset's downside deviation. The ratio was named after Frank A. Sortino.'

Applying this definition to our asset in some examples:- The downside risk / excess return profile over 5 years of ProShares UltraPro QQQ is 0.7, which is lower, thus worse compared to the benchmark SPY (0.85) in the same period.
- During the last 3 years, the ratio of annual return and downside deviation is 0.17, which is lower, thus worse than the value of 0.63 from the benchmark.

'The Ulcer Index is a technical indicator that measures downside risk, in terms of both the depth and duration of price declines. The index increases in value as the price moves farther away from a recent high and falls as the price rises to new highs. The indicator is usually calculated over a 14-day period, with the Ulcer Index showing the percentage drawdown a trader can expect from the high over that period. The greater the value of the Ulcer Index, the longer it takes for a stock to get back to the former high.'

Using this definition on our asset we see for example:- Looking at the Ulcer Ratio of 43 in the last 5 years of ProShares UltraPro QQQ, we see it is relatively higher, thus worse in comparison to the benchmark SPY (9.32 )
- Looking at Downside risk index in of 52 in the period of the last 3 years, we see it is relatively greater, thus worse in comparison to SPY (10 ).

'A maximum drawdown is the maximum loss from a peak to a trough of a portfolio, before a new peak is attained. Maximum Drawdown is an indicator of downside risk over a specified time period. It can be used both as a stand-alone measure or as an input into other metrics such as 'Return over Maximum Drawdown' and the Calmar Ratio. Maximum Drawdown is expressed in percentage terms.'

Applying this definition to our asset in some examples:- The maximum drop from peak to valley over 5 years of ProShares UltraPro QQQ is -81.7 days, which is smaller, thus worse compared to the benchmark SPY (-33.7 days) in the same period.
- Looking at maximum DrawDown in of -81.7 days in the period of the last 3 years, we see it is relatively lower, thus worse in comparison to SPY (-24.5 days).

'The Drawdown Duration is the length of any peak to peak period, or the time between new equity highs. The Max Drawdown Duration is the worst (the maximum/longest) amount of time an investment has seen between peaks (equity highs). Many assume Max DD Duration is the length of time between new highs during which the Max DD (magnitude) occurred. But that isn’t always the case. The Max DD duration is the longest time between peaks, period. So it could be the time when the program also had its biggest peak to valley loss (and usually is, because the program needs a long time to recover from the largest loss), but it doesn’t have to be'

Which means for our asset as example:- The maximum days below previous high over 5 years of ProShares UltraPro QQQ is 644 days, which is higher, thus worse compared to the benchmark SPY (488 days) in the same period.
- Looking at maximum days under water in of 644 days in the period of the last 3 years, we see it is relatively larger, thus worse in comparison to SPY (488 days).

'The Average Drawdown Duration is an extension of the Maximum Drawdown. However, this metric does not explain the drawdown in dollars or percentages, rather in days, weeks, or months. The Avg Drawdown Duration is the average amount of time an investment has seen between peaks (equity highs), or in other terms the average of time under water of all drawdowns. So in contrast to the Maximum duration it does not measure only one drawdown event but calculates the average of all.'

Which means for our asset as example:- Looking at the average time in days below previous high water mark of 193 days in the last 5 years of ProShares UltraPro QQQ, we see it is relatively larger, thus worse in comparison to the benchmark SPY (123 days)
- During the last 3 years, the average days under water is 288 days, which is higher, thus worse than the value of 180 days from the benchmark.

Historical returns have been extended using synthetic data.
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- Note that yearly returns do not equal the sum of monthly returns due to compounding.
- Performance results of ProShares UltraPro QQQ are hypothetical and do not account for slippage, fees or taxes.